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GCF of 784/83, 670/823

Created By : Veerendra
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023

Use our free GCF of Fractions Calculator tool to compute the GCF of 784/83, 670/823 i.e 2/68309 easily. The following is the detailed procedure to determine the greatest common factor of fractions 784/83, 670/823.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

What is the GCF of 784/83,670/823?

Given fractions are 784/83,670/823

To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by

GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators

In the fractions 784/83,670/823, numerators are 784,670

Denominators are 83,823

The GCF of 784,670 is 2 .

LCM of 83,823 is 68309.

The greatest common factor of 784/83,670/823 = [GCF of 784,670]/[LCM of 83,823]= 2/68309

Therefore, the GCF of 784/83,670/823 is 2/68309.

Greatest Common Factor of 784,670

To find the highest common factor of 784,670, we have to find the factors of both numbers and list the highest common factor.

The factors of 784 are 1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392, 784

The factors of 670 are 1, 2, 5, 10, 67, 134, 335, 670

The HCF of 784,670 is 2.

Lets's calculate GCF of 784,670

Greatest Common Factor (GCF) of 784,670 By Common Division

2 784, 670
392, 335

∴ So the GCF of the given numbers is 2 = 2

Greatest Common Factor of 784,670 By Matching Biggest Common Factor Method

Greatest Common Factor of 784,670 By Matching Biggest Common Factor Method

Now, list down the factors of 784

:

1,2,4,7,8,14,16,28,49,56,98,112,196,392,784

Now, list down the factors of 670

:

1,2,5,10,67,134,335,670

Greatest Common Factor

We found the factors 784,670 . The biggest common factor number is the GCF number.
So the greatest common factor 784,670 is 2.

Lets's calculate LCM of 83,823

Lowest Common Multiple of 83,823 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 68309

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/68309

Therefore, the GCF of Fractions 784/83,670/823 is 2/68309

Least Common Multiple of 83,823 with GCF Formula

Least Common Multiple of 83,823 with GCF Formula

The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 83,823 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(83,823) = 1

common factors(in case of two or more numbers have common factors) = 1

GCF(83,823) x common factors =1 x 1 = 1

LCM(83,823) = ( 83 × 823 ) / 1

LCM(83,823) = 68309 / 1

LCM(83,823) = 68309


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FAQs on GCF of Fractions of 784/83, 670/823

1. What is the HCF of 784,670?

The HCF of 784,670 is 2

2. What is the GCF of a fraction?

The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.

3. How to find GCF in Fractions?

Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.

4. What is the GCF of Fractions for 784/83, 670/823?

Answer: GCF of Numerators as per given numbers 784/83, 670/823 is

GCF of Numerators i.e. for 784,670 is 2

LCM of denominators i.e. for 83,823 is 68309.

Thus, GCF of Fractions is 2/68309.Finally, GCF of Fractions for 784/83, 670/823 is 2/68309.